Some unified formulas involving generalized-Apostol-type-Gould-Hopper polynomials and multiple power sums

Volume 19, Issue 2, pp 97--115 http://dx.doi.org/10.22436/jmcs.019.02.04

Publication Date: May 03, 2019 Submission Date: August 21, 2017 Revision Date: June 03, 2018 Accteptance Date: April 09, 2019

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Authors

Serkan Araci - Department of Economics, Faculty of Economics, Administrative and Social Sciences, Hasan Kalyoncu University, TR-27410, Gaziantep, Turkey. Mumtaz Riyasat - Department of Mathematics, Faculty of Science, Aligarh Muslim University, Aligarh, India. Subuhi Khan - Department of Mathematics, Faculty of Science, Aligarh Muslim University, Aligarh, India. Shahid Ahmad Wani - Department of Mathematics, Faculty of Science, Aligarh Muslim University, Aligarh, India.

Abstract

The article aims to introduce a new unified class of generalized Apostol type polynomials. Further, under a slight modification on the parameters associated to the generalized Apostol type and generalized Gould-Hopper polynomials and by the use of generating method, we introduce a new class of generalized-Apostol-type-Gould-Hopper polynomials. We state some quasi-monomial properties for a new class of extensions of generalized Apostol type polynomials as well as, some summation, multiplication and explicit formulae which connect this polynomial class with the \(\lambda\)-Stirling numbers of second kind and generalized Hurwitz zeta function. Some general symmetry identities involving multiple power sums are also established. The new class of polynomials contains as its special cases, not only the generalized-Gould-Hopper-Apostol-Bernoulli, Euler and Genocchi polynomials but many more known smaller classes of polynomials. Finally, the these polynomials are framed within the context of generalized modified Milne-Thomson's polynomials.

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Keywords

• Generalized-Apostol-type-Gould-Hopper polynomials
• monomiality principle
• summation formula
• multiplication formulae
• symmetry identities

MSC

•  11B68
•  05A10
•  11B65

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